1. 2009 Mathematics Standards of Learning Training Institutes Algebra I Virginia Department of Education

2. "We can't solve problems by using the same kind of thinking we used when we created them." Albert Einstein

3. A Time for Change: Algebra 1 Reporting categories are unchanged Expressions and Operations Equations and Inequalities Functions (previously Relations and Functions) Statistics Many Standards of Learning (SOL) have been consolidated – previously 18 standards, now 11 standards Reporting categories now have consecutively numbered SOL

4. Some content moved to grades 6-8 Converting numbers between scientific and standard notations (7.1, 8.1) Estimating non-perfect square roots (8.5) Stating domain and range of a relation (8.17) Mean, median and mode (5.16, 6.15) Some content moved to Math Analysis Matrices A Time for Change: Algebra 1

5. Raising the Level of Rigor Increased content in Algebra 1 Content taught through mathematical modeling No upward spiraling of content Use of appropriate and accurate mathematics vocabulary

6. Raising the Level of Rigor (continued) Removal of “limiters” Previous Statement: Translate verbal expressions into algebraic expressions with three or fewer terms. New Statement: Translate verbal quantitative situations into algebraic expressions and vice versa.

7. Expressions and Operations STANDARD A.1 The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variable.

8. Expressions and Operations STANDARD A.2 The student will perform operations on polynomials, including a) applying the laws of exponents to perform operations on expressions; b) adding, subtracting, multiplying, and dividing polynomials; and (continued)

9. STANDARD A.2 (continued) c) factoring completely first- and second- degree binomials and trinomials in one or two variables. Graphing calculators will be used as a tool for factoring and for confirming algebraic factorizations. Expressions and Operations

10. Points of Interest for A.2 from the Proposed Curriculum Framework Operations with polynomials can be represented concretely, pictorially, and symbolically. VDOE Algeblocks Training Video http://www.vdoe.whro.org/A_Blocks05/index.html

11. (2x + 5) + (x – 4) = 3x + 1

12. Expressions and Operations STANDARD A.3 The student will express the square roots and cube roots of whole numbers and the square root of a monomial algebraic expression in simplest radical form. (2001 SOL)…approximating square roots to the nearest tenth.

13. Points of Interest for A.3 from the Proposed Curriculum Framework Increased in the rigor of the terminology Radicand (argument) Principal square root

14. Equations & Inequalities STANDARD A.4 The student will solve multistep linear and quadratic equations in two variables, including a) solving literal equations (formulas) for a given variable; b) justifying steps used in simplifying expressions and solving equations, using field properties and axioms of equality that are valid for the set of real numbers and its subsets; (continued)

15. STANDARD A.4 (continued) c) solving quadratic equations algebraically and graphically; d) solving multistep linear equations algebraically and graphically; e) solving systems of two linear equations in two variables algebraically and graphically; and f) solving real-world problems involving equations and systems of equations Equations & Inequalities

16. Graphing calculators will be used both as a primary tool in solving problems and to verify algebraic solutions. Equations & Inequalities

17. Points of Interest for A.4 from the proposed Curriculum Framework Set builder notation may be used Example: Terminology for solutions: roots instead of x-intercepts Example: Find the roots of

18. Equations & Inequalities STANDARD A.5 The student will solve multistep linear inequalities in two variables, including a) solving multistep linear inequalities algebraically and graphically; b) justifying steps used in solving inequalities, using axioms of inequality and properties of order that are valid for the set of real numbers and its subsets; (continued)

19. STANDARD A.5 (continued) c) solving real-world problems involving inequalities; and d) solving systems of inequalities. Equations & Inequalities

20. STANDARD A.6 The student will graph linear equations and linear inequalities in two variables, including a) determining the slope of a line when given an equation of the line, the graph of the line, or two points on the line. Slope will be described as rate of change and will be positive, negative, zero, or undefined; and (continued) Equations & Inequalities

21. STANDARD A.6 (continued) b) writing the equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line. Example: Write the equation of the line shown in the following graph. Equations & Inequalities

22. Points of interest for A.6 from the proposed Curriculum Framework Relating the graphing of a line to transformations of a parent function (translations, dilations, reflections) B A B A

23. Relationships between the slopes of perpendicular lines Slope for line A: Slope for line B: A B Points of interest for A.6 from the proposed curriculum framework

24. Functions STANDARD A.7 The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including a) determining whether a relation is a function; b) domain and range; (continued)

25. STANDARD A.7 (continued) c) zeros of a function; d) x- and y-intercepts; e) finding the values of a function for elements in its domain; and f) making connections between and among multiple representations of functions including concrete, verbal, numeric, graphic, and algebraic. Functions

26. STANDARD A.8 The student, given a situation in a real-world context, will analyze a relation to determine whether a direct or inverse variation exists, and represent a direct variation algebraically and graphically and an inverse variation algebraically.

27. Statistics STANDARD A.9 The student, given a set of data, will interpret variation in real-world contexts and calculate and interpret mean absolute deviation, standard deviation, and z-scores.

28. Statistics STANDARD A.10 The student will compare and contrast multiple univariate data sets using box-and- whisker plots.

29. Statistics STANDARD A.11 The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve real-world problems using mathematical models. Mathematical models will include linear and quadratic functions.